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Class preserving automorphisms of Blackburn groups

Published online by Cambridge University Press:  09 April 2009

Allen Herman
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina Saskatchewan S4S 0A2, Canada, e-mail: aherman@math.uregina.ca
Yuanlin Li
Affiliation:
Department of Mathematics, Brock University, St. Catharine's, Ontario L2S 3A1, Canada, e-mail: yli@brocku.ca
Corresponding
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Abstract

In this article, a Blackburn group refers to a finite non-Dedekind group for which the intersection of all nonnormal subgroups is not the trivial subgroup. By completing the arguments of M. Hertweck, we show that all conjugacy class preserving automorphisms of Blackburn groups are inner automorphisms.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Blackburn, N.Finite groups in which the nonnormal subgroups have nontrivial intersection’, J. Algebra 3 (1966), 3037.CrossRefGoogle Scholar
[2]Hertweck, M., Contributions to the integral representation theory of groups (Habilitationsschrift, University of Stuttgart, 2004), available at elib.uni-stuttgart.de/opus/volltexte/2004/1638/Google Scholar
[3]Huppert, B., Endliche Gruppen I (Springer, New York, 1967).CrossRefGoogle Scholar
[4]Jackowski, S. and Marciniak, Z.Group automorphisms inducing the identity map on cohomology’, J. Pure Appl. Algebra 44 (1987), 241250.CrossRefGoogle Scholar
[5]Li, Y., Parmenter, M. M. and Sehgal, S. K.On the normalizer property for integral group rings’, Comm. Algebra 27 (1999), 42174223.CrossRefGoogle Scholar
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